Engineering Maths - Probability

11. An urn contains 5 red and 10 black balls. Eight of them are placed in another urn. The chance that the latter then contains 2 red and 6 black balls is

  • Option : A
  • Explanation : Number of ways in which 8 balls can be drawn
    out of 15 is 15C8
    Number of ways of drawing 2 red balls is 5C2
    and corresponding to each of these 5C2 ways
    of drawing a red ball, there are IOC5 ways of
    drawing 6 black balls.
    Hence total number of ways in which 2 red
    and 6 black balls can be drawn = 5C2 X 10C6

    Required Probability = Probability

                                               =  140/429

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12. A has one share in a lottery in which there is 1 prize and 2 blanks; B has three shares in a lottery in which there are 3 prizes and 6 blanks; compare the probability of A's success to that of B's success is

  • Option : A
  • Explanation : A can draw a ticket in 3C1 = 3 ways.
    Number of cases in which A can get a prize
    is clearly 1.

    Probability of A's success = 1/3

    Again B can draw a ticket in   Probability

    Number of ways in which B gets all blanks

                                                  Probability

    Number of ways of getting a prize
                                                                 = 84 - 20 = 64

    Thus, probability of B's success  =        Probability

    A's probability of success : B's probability
    of success

       Probability

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13. If A and B are independent, then A and B' are also

  • Option : A
  • Explanation : P(A ∩ B') =  P(A) - P(A ∩ B)

                       = P(A) - P(A) P(B)

                      = P(A) (1 - P(B)) = P(A) P(B')

    Hence, A and B' are independent.

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14. The chance that a leap year selected at random will contain 53 Sundays is

  • Option : B
  • Explanation : A leap year consists of 366 days, so that there
    are 52 full weeks (and hence 52 Sundays) and
    two extra days. These two days can be
    (i) Monday, Tuesday
    (ii) Tuesday, Wednesday,
    (iii) Wednesday, Thursday
    (iv) Thursday, Friday
    (v) Friday, Saturday
    (vi) Saturday, Sunday
    (vii) Sunday, Monday
    Of these 7 cases. the last two are favourable

    Required probability = 2/7

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15. P(A ∩ B'/C) + P(A ∩ B/C) = P(A/C)

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